Image Processing Reference
In-Depth Information
The residual at time-point
t
between measured image
S
t
and expected image
S
t
=
S
t−
1
(
ˆ
t−
1
) stems from the fact that the necessary spatial regularization
during optimization of (
2
) outweighs the available image information. Mismatch-
ing regions lack the information that could drive an image-based deformation
model. They should thus be subjected to stronger temporal consistency. This
leads us to propose the spatially adaptive temporal smoothing prior
p
t
=
˃
x
1
v
u
+
˃
t
S
t
−
S
t
S
t
v
t
−S
t
−
(4)
˃
x
+
˃
t
Figure
2
gives an illustration of the proposed adaptive regulartization.
3 Experiments
We perform two sets of experiments to validate the proposed method: first on
two sets of simplified synthetic models of cortical folding and secondly on a
publicly available dataset of human brain development. We show that the pro-
posed method is capable of accurately representing the deformation in all cases
and results in smoother deformation fields than simple pairwise registration.
We further show that using a spatio-temporal prior results in deformation mod-
els that faithfully model continuous developmental processes by evaluating its
reconstruction error on unseen data.
In all experiments, the parameters of (
2
) and (
4
)aresetto
˃
i
,˃
x
,˃
s
=1,
˃
t
=
.
5.
3.1 Synthetic Cortical Folding
We generate two sets of synthetic cortical folding sequences from two parametric
models containing gray and white matter (Figure
3
). The models represent the
formation of a single respectively two sulci. We generate 20 such sequences of
Fig. 2.
Sketch of the computation of the spatially adaptive prior
p
2
. The residual
between
˜
S
t
3
(orange) and
S
t
3
is indicated in gray.
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